(display "\n========================================\n")
(define (variable? x) (symbol? x))

(define (same-variable? v1 v2)
    (and (variable? v1) (variable? v2) (eq? v1 v2)))

; (define (make-sum a1 a2) (list '+ a1 a2))

; (define (make-product m1 m2) (list '* m1 m2))

(define (sum? x)
    (and (pair? x) (eq? (car x) '+)))

(define (addend s) (cadr s))

(define (augend s) (caddr s))

(define (product? x)
    (and (pair? x) (eq? (car x) '*)))

(define (multiplier p) (cadr p))

(define (multiplicand p) (caddr p))

(define (=number? exp num)
    (and (number? exp) (= exp num)))

(define (make-sum a1 a2)
    (cond   ((=number? a1 0) a2)
            ((=number? a2 0) a1)
            ((and (number? a1) (number? a2)) (+ a1 a2))
            (else (list '+ a1 a2))))

(define (make-product m1 m2)
    (cond   ((or (=number? m1 0) (=number? m2 0)) 0)
            ((=number? m1 1) m2)
            ((=number? m2 1) m1)
            ((and (number? m1) (number? m2)) (* m1 m2))
            (else (list '* m1 m2))))

(define (make-exponentiation base exponent)
    (cond   ((= exponent 0) 1)
            ((= exponent 1) base)
            (else (list '** base exponent))))

(define (exponentiation? x)
    (and (pair? x) (eq? (car x) '**)))

(define (base x)
    (cadr x))

(define (exponent x)
    (caddr x))

(define (deriv exp var)
    (cond   ((number? exp) 0)
            ((variable? exp)
                (if (same-variable? exp var) 1 0))
            ((sum? exp)
                (make-sum (deriv (addend exp) var)
                          (deriv (augend exp) var)))
            ((product? exp)
                (make-sum
                    (make-product (multiplier exp)
                                  (deriv (multiplicand exp) var))
                    (make-product (deriv (multiplier exp) var)
                                  (multiplicand exp))))
            ((exponentiation? exp)
                (let ((n (exponent exp))
                      (u (base exp)))
                    (make-product
                        n
                        (make-product
                            (make-exponentiation
                                u
                                (- n 1))
                            (deriv u var)))))
            (else
                (error "Unknow exception type -- DERIV" exp))))

; (display (deriv '(** x 0) 'x))
; (display (deriv '(** x 1) 'x))
; (display (deriv '(** x 2) 'x))
(display (deriv '(** x 3) 'x))

(display "\n========================================\n")
